This is heavy on the earlier years of this decade, but that's mostly because enough time has gone by to really consider these films.
1. Donnie Darko
2. Adaptation.
3. You Can Count On Me
4. Ghost World
5. About Schmidt
6. Memento
7. Requiem for a Dream
8. Capturing the Friedmans
9. A.I.
10. Talk to Her
11. George Washington
12. Lost in Translation
13. Together/Lilja 4-Ever (tie-both by Moodysson)
14. In the Bedroom
15. High Fidelity
16. Kill Bill: The Whole Bloody Affair
17. Bowling for Columbine
18. Before Sunset
19. The Squid and the Whale
20. Brokeback Mountain
1-15 I feel pretty confident about. 16-20 might change.
Feel free to submit your own list...